Stress analysis review for stress analysis Engineer as an introduction to stress analysis theory. It gives an idea about the code equations and basic stress analysis concept

2. Stress Analysis Review
References:
• ASME B31.3
• Piping Design Handbook, Nayyar, 7th Edition
• COADE Seminar, 2013
• Piping Design and Engineering, Grinnell, 3rd Edition
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3. Stress Vs. Strain Curve
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Tensile Strength

4. Stresses of Thin Straight Pipe
• Longitudinal stress: 𝑆𝐿 = (
𝐹
𝐴
+
𝑃𝐷
4𝑡
+
𝑀
𝑍
)2+(2
𝑇
2𝑧
)2
• Hoop stress: 𝑆𝐻 =
𝑃𝐷
2𝑡
• Radial stress 𝑆𝑅 = Zero. Can be ignored because of the thin wall
assumption.
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5. Failure Theories
How much of the previous stresses should fail the pipe?
• Maximum distortion theory (von Mises):
• Failure occurs when 𝜎𝑣 = 𝑆𝑦
• Max shear stress theory (Tresca)
• Failure occurs when 𝜎𝑚𝑎𝑥 − 𝜎𝑚𝑖𝑛 = Ʈ𝑚𝑎𝑥 =
𝑆𝑦
2
• Max Stress – Rankine Theory
• Failure occurs when 𝜎𝑚𝑎𝑥= 𝑆𝑦
Where,
𝜎𝑚𝑎𝑥 : Maximum of hoop or longitudinal stresses
𝜎𝑚𝑖𝑛 : Equals radial Stress or compressive longitudinal stress
𝑆𝑦 : Material Yield strength,
Ʈ𝑚𝑎𝑥 : Maximum Shear Stresses

6. CODE STRESS TYPES
• Sustained:
• While the whole system is not operating and filled with the fluid.
• Only considers weight or pressure.
• Causes primary stresses and peak stresses in fittings
• Operating:
• While the system is operating totally or partially according to process requirements scenarios.
• Considers the primary loads (weight and pressure), operating thermal loads.
• Causes primary, secondary and peak stresses
• Occasional:
• While the system is experiencing an abnormal conditions, such as relief valve discharge , wind or
earthquake .
• Consider the operating and sustained loads while occasional loads is occurring
• Causes primary, secondary, peak and dynamic (or equivalent static) stresses
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7. Creep Deformation
• Is the tendency of a material to deform permanently under the influence of mechanical stresses. It
can occur as a result of long-term exposure to high levels of stress that are still below the yield
strength of the material. Creep is more severe in materials that are subjected to heat for long periods.
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8. Prevent the piping system to be too constrained
(rigid)
• Prevent failure of piping or supports from overstress or
fatigue
• Prevent detrimental stresses or distortion in piping and
valves and connected equipment.
• Compute the stress range at any point due to
displacements and ensure it does not exceed the allowable.
• Compute reaction forces and moments and ensure it is not
detrimental to supports or connected equipment.
Prevent the piping system to be too flexible
• Prevent leakage at joints
• Compute movement of the piping to be within
prescribed limits
• Unintentional disengagement of piping from
supports
• Excessive piping sagging in piping requiring
drainage slope or pipe subject to creep
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Requirements Para. 319.1

9. Reactions
• Sustained loads + Operating (thermal) loads + Occasional (if applicable) used to design Restraints
• Evaluated against allowable equipment nozzle loads, supports allowable loads.
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Para. 319.5

10. Means of Increasing Flexibility
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11. Suggested Pipe Support Spacing
• For horizontal straight runs of standard and
heavier pipe at maximum operating temperature
of 750°F (400°C).
• Does not apply where span calculations are made
or where there are concentrated loads between
supports, such as flanges, valves, specialties, etc.
• The spacing is based on a fixed beam support with
a bending stress not exceeding 2,300 psi (15.86
MPa) and insulated pipe filled with water or the
equivalent weight of steel pipe for steam, gas, or
air service, and the pitch of the line is such that a
sag of 0.1 in. (2.5 mm) between supports is
permissible.
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ASME B31.1

12. Pipe Supporting - Span
Pipe Support Span calculation based on deflection
Pipe support span is a decision that faces the designer in most pipe supporting
jobs. As a guide to the selection of support spacing, the following equation
based on permissible mid span deflection is offered.
The permissible mid-span deflection, y, concept is one technique commonly
selected for support spacing. This technique is based on a specified mid-span,
y deflection of the supported pipe considering the pipe, contents, and
insulation weights. The equation is:
L= [y.E.I / 22.5.W]¼
where:
L = pipe support spacing, feet,
y = permissible mid-span deflection, inches
E = modulus of elasticity at design temperature, lb/in (TABLE C-6(
I = moment of inertia of pipe.
W = weight of supported pipe, including pipe, contents, insulation, lb/ft.

13. Pipe Supporting - Span
An example of the deflection pipe span approach is:
What is the span of a seamless ASTM A106 Grade B, 6.625 inch OD, 0.28 inch wall thick, water filled pipe with 3 inch of
insulation with a design temperature of 400 F? The specifications limit the mid-span deflection to 0.25 inch.
Solution:
Determine the uniform load, pounds per foot.
Pipe = 19.0 lbs per ft
Water = 12.5 lbs per ft
Insulation = 7.6 lbs per ft ( 85 % Magnesia Calcium Silicate)
then ,W = 39.1 lb per ft
I = ( π /64)(Do
4 – Di
4), Do = 6.625, Di = 6.065
I = 28.14 in4
E = 27.7 x 106 psi, Table C-6, C ≤ 0.3 at 400°F.
finally, L = [ 0.25x27.7x106 x28.14/(17. 1x39. 1)]1/4
L = 23 feet span
The pipe support spacing would be 23 feet with a mid span deflection of 1/4 inch.

14. Piping Support
• More supports are provided in MSS-SP-58 standard
• Gray iron is not recommended if the piping may be subject to impact-type
loading resulting from pulsation or vibration. Ductile and malleable iron
may be used for pipe and beam clamps, hanger flanges.
• Steel of an unknown specification may be used for pipe supporting
elements that are not welded directly to pressure containing piping
components.
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Para. 321

15. Resilient Supports
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Para. 321.2.3
• Springs shall be provided with means to prevent misalignment, buckling, or eccentric loading of
the springs, and to prevent unintentional disengagement of the load.
• Constant-support spring hangers provide a substantially uniform supporting force throughout the
range of travel.
• Means shall be provided to prevent excessive deflections. It is recommended that all spring
hangers be provided with position indicators.

16. Pipe Supporting Problems
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